The periodic waves of intensities I1 and I2 pass through

The periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

1. I₁ + I₂
2. (√I₁ + √I₂)²
3. (√I₁ - √I₂)²
4. 2(I₁ + I₂)

Correct Option: D

The resultant intensity of two periodic waves at a point is given by
I = I₁ + I₂ + 2√I₁ I₂ .cosφ
Resultant intensity is maximum if
cos φ = –1
i.e. I_max = I₁ + I₂ + 2√I₁ I₂
Resultant intensity is minimum if
cos φ = +1
i.e, I_min = I₁ + I₂ - 2√I₁ I₂
Therefore, the sum of the maximum and minimum intensities is I_max + I_min
= I₁ + I₂ + 2√I₁ I₂ + I₁ + I₂ - 2√I₁ I₂
= 2 (I₁ + I₂)

Wave Optics

Optics

Correct Option: D